cellular automaton

(CA, plural "- automata") A regular
spatial lattice of "cells", each of which can have any one of
a finite number of states. The state of all cells in the
lattice are updated simultaneously and the state of the entire
lattice advances in discrete time steps. The state of each
cell in the lattice is updated according to a local rule which
may depend on the state of the cell and its neighbors at the
previous time step.

Each cell in a cellular automaton could be considered to be a
finite state machine which takes its neighbours' states as
input and outputs its own state.